Hi there ecs87,
It's vital that all your transactions are entered correctly for your books to be well balanced. QuickBooks Online is a great tool able to help you keep track of sales and expenses so you can see the profit of your business. I can point you in the right direction for reports.
If you're looking at seeing your total income, you can take a look at either the profit and loss, which will show you the total sales for a period by account in your chart of accounts, or if you'd like to see it in more detail, you can click on the Profit and loss detail report. Both of those reports can be found in the Business Overview section of the Reports tab.
Another report that could be useful to sort out government, charitable or religious organizations would be a Transaction list by Customer report, located in the Sales and Customers section of the reports tab. You can click the option to filter, then select only the customers that would fall into the categories needed so that this report only shows transactions from them. You can also filter for specific transaction types to help narrow down the ones not needed.
To see the transactions separated by tax code used, you can click on the Transaction Detail by Tax Code report located in the Sales tax section of the reports tab. There isn't a way to separate reasons for exemptions within QuickBooks Online, so you'd need to analyze each transaction marked as exempt to keep track of it outside of the program.
There also isn't the option to sort out transactions by their shipping destination. i can see that this would be an option you'd like to see for reports. I recommend you leave feedback in the system for the developers by clicking on the Gear Icon, then Feedback. The comments made in that section are taken into consideration when designing new features for QuickBooks Online.
if you have any other questions, feel free to reach out here.